Emily Analysis

**Table 1. Baseline Characteristics**
Characteristic	Overall N = 180¹	ABC N = 30¹	ACB N = 30¹	BAC N = 30¹	BCA N = 30¹	CAB N = 30¹	CBA N = 30¹	p-value²
Age (years)	32 (8) [18, 45]	33 (8) [19, 44]	31 (7) [18, 42]	31 (7) [20, 44]	33 (8) [19, 45]	32 (7) [21, 44]	31 (7) [20, 44]	0.6
Race								0.9
Black	64 (36%)	12 (40%)	13 (43%)	12 (40%)	10 (33%)	8 (27%)	9 (30%)
White	52 (29%)	8 (27%)	9 (30%)	7 (23%)	7 (23%)	12 (40%)	9 (30%)
Other	64 (36%)	10 (33%)	8 (27%)	11 (37%)	13 (43%)	10 (33%)	12 (40%)
Female	81 (45%)	13 (43%)	11 (37%)	16 (53%)	14 (47%)	12 (40%)	15 (50%)	0.8
¹ Mean (SD) [Min, Max]; n (%)
² Kruskal-Wallis rank sum test; Pearson’s Chi-squared test

preliminary assessment and comparison of systemic and local Pharmacokinetics (PK) of Pill A, Gel B, and Gel C

No apparent difference in starting value by period or treatment, so looking at change from baseline in PK

Carryover effects and period were excluded for parsimony, as the likelihood ratio test indicated that they did not significantly improve model fit

Notation: \(k =\) subject, \(i =\) treatment, \(j =\) period,

\[ \begin{align} Y_{ijk} &= \mu + b_{ik} + \tau_{ij} + \varepsilon_{ijk},\\ b_{ik} &\sim N(0, \sigma_k^2), \\ \varepsilon_{ij} &\sim N(0, \sigma^2), \end{align} \]

Blood PK Change by Treatment

Findings: Significantly less decrease in gels vs pill A

## Data: merged
## Models:
## model: bloodVL_change ~ treatment + period + (1 | ptid)
## model_large: bloodVL_change ~ treatment + sequence_ind + period + (1 | ptid)
##             npar    AIC    BIC  logLik -2*log(L)  Chisq Df Pr(>Chisq)
## model          7 4926.1 4956.1 -2456.0    4912.1                     
## model_large    8 4927.2 4961.5 -2455.6    4911.2 0.8686  1     0.3513

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bloodVL_change ~ treatment + period + (1 | ptid)
##    Data: merged
## 
## REML criterion at convergence: 4896.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.7874 -0.6001  0.0430  0.6241  2.4126 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ptid     (Intercept)  41.2     6.419  
##  Residual             489.2    22.117  
## Number of obs: 540, groups:  ptid, 180
## 
## Fixed effects:
##                Estimate Std. Error      df t value             Pr(>|t|)    
## (Intercept)     122.243      2.181 513.694  56.040 < 0.0000000000000002 ***
## treatmentGel B  -10.889      2.331 356.000  -4.671          0.000004264 ***
## treatmentGel C  -11.656      2.331 356.000  -4.999          0.000000904 ***
## periodperiod2    -1.533      2.331 356.000  -0.658                0.511    
## periodperiod3    -1.711      2.331 356.000  -0.734                0.463    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) trtmGB trtmGC prdpr2
## treatmntGlB -0.534                     
## treatmntGlC -0.534  0.500              
## periodperd2 -0.534  0.000  0.000       
## periodperd3 -0.534  0.000  0.000  0.500

Characteristic	Beta	95% CI	p-value
treatment
Pill A	—	—
Gel B	-11	-15, -6.3	<0.001
Gel C	-12	-16, -7.1	<0.001
period
period1	—	—
period2	-1.5	-6.1, 3.1	0.5
period3	-1.7	-6.3, 2.9	0.5
Abbreviation: CI = Confidence Interval

Skin PK Change by Treatment

Findings: Significantly less decrease in gels vs pill A

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: skinVL_change ~ treatment + sequence_ind + period + (1 | ptid)
##    Data: merged
## 
## REML criterion at convergence: 5390.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.4199 -0.5952  0.0426  0.7273  3.2412 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ptid     (Intercept)    0      0.00   
##  Residual             1339     36.59   
## Number of obs: 540, groups:  ptid, 180
## 
## Fixed effects:
##                Estimate Std. Error       df t value             Pr(>|t|)    
## (Intercept)    205.2176     4.0145 534.0000  51.119 < 0.0000000000000002 ***
## treatmentGel B -32.4056     3.8570 534.0000  -8.402   0.0000000000000004 ***
## treatmentGel C -41.9222     3.8570 534.0000 -10.869 < 0.0000000000000002 ***
## sequence_ind    -0.9472     1.9285 534.0000  -0.491                0.624    
## periodperiod2    2.5000     3.8570 534.0000   0.648                0.517    
## periodperiod3    1.2722     3.8570 534.0000   0.330                0.742    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) trtmGB trtmGC sqnc_n prdpr2
## treatmntGlB -0.480                            
## treatmntGlC -0.480  0.500                     
## sequence_nd -0.480  0.000  0.000              
## periodperd2 -0.480  0.000  0.000  0.000       
## periodperd3 -0.480  0.000  0.000  0.000  0.500
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

## Data: merged
## Models:
## model: skinVL_change ~ treatment + period + (1 | ptid)
## model_large: skinVL_change ~ treatment + sequence_ind + period + (1 | ptid)
##             npar    AIC    BIC  logLik -2*log(L)  Chisq Df Pr(>Chisq)
## model          7 5428.4 5458.5 -2707.2    5414.4                     
## model_large    8 5430.2 5464.5 -2707.1    5414.2 0.2439  1     0.6214

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: skinVL_change ~ treatment + period + (1 | ptid)
##    Data: merged
## 
## REML criterion at convergence: 5394.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.4223 -0.5960  0.0491  0.7339  3.2176 
## 
## Random effects:
##  Groups   Name        Variance                 Std.Dev.      
##  ptid     (Intercept)    0.0000000000000001573  0.00000001254
##  Residual             1336.9992661820692774199 36.56500056314
## Number of obs: 540, groups:  ptid, 180
## 
## Fixed effects:
##                Estimate Std. Error      df t value             Pr(>|t|)    
## (Intercept)     204.270      3.518 535.000  58.057 < 0.0000000000000002 ***
## treatmentGel B  -32.406      3.854 535.000  -8.408 0.000000000000000381 ***
## treatmentGel C  -41.922      3.854 535.000 -10.877 < 0.0000000000000002 ***
## periodperiod2     2.500      3.854 535.000   0.649                0.517    
## periodperiod3     1.272      3.854 535.000   0.330                0.741    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) trtmGB trtmGC prdpr2
## treatmntGlB -0.548                     
## treatmntGlC -0.548  0.500              
## periodperd2 -0.548  0.000  0.000       
## periodperd3 -0.548  0.000  0.000  0.500
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

Characteristic	Beta	95% CI	p-value
treatment
Pill A	—	—
Gel B	-32	-40, -25	<0.001
Gel C	-42	-49, -34	<0.001
period
period1	—	—
period2	2.5	-5.1, 10	0.5
period3	1.3	-6.3, 8.8	0.7
Abbreviation: CI = Confidence Interval

Characteristic	Beta	SE	95% CI	p-value
treatment
Pill A	—	—	—
Gel B	-32	3.85	-40, -25	<0.001
Gel C	-42	3.85	-49, -34	<0.001
period
period1	—	—	—
period2	2.5	3.85	-5.1, 10	0.5
period3	1.3	3.85	-6.3, 8.8	0.7
Abbreviations: CI = Confidence Interval, SE = Standard Error

assess the correlation of PK with adherence measures and the occurrence of adverse events

Carryover effects and period were excluded for parsimony, as the likelihood ratio test indicated that they did not significantly improve model fit

Q: include treatment X adherence and treatment X AE interaction terms???

Skin PK

Skin/Blood PK ~ Random Intercept (Subject) + Treatment + Adherence + Carryover + Period

##             Model df      AIC      BIC    logLik   Test  L.Ratio p-value
## model           1  7 5307.160 5337.201 -2646.580                        
## model_large     2 10 5312.149 5355.064 -2646.074 1 vs 2 1.011282  0.7985

## Linear mixed-effects model fit by maximum likelihood
##   Data: merged 
##       AIC      BIC   logLik
##   5307.16 5337.201 -2646.58
## 
## Random effects:
##  Formula: ~1 | ptid
##         (Intercept) Residual
## StdDev: 0.003649564 32.52911
## 
## Fixed effects:  skinVL_change ~ treatment + overall_adhere + overall_safety 
##                     Value Std.Error  DF    t-value p-value
## (Intercept)     162.22787  7.582825 356  21.394119       0
## treatmentGel B  -24.41464  3.625130 356  -6.734832       0
## treatmentGel C  -36.99593  3.543320 356 -10.441036       0
## overall_adhere    1.81506  0.274724 356   6.606870       0
## overall_safety1 -55.77639  5.201704 356 -10.722715       0
##  Correlation: 
##                 (Intr) trtmGB trtmGC ovrll_
## treatmentGel B  -0.509                     
## treatmentGel C  -0.443  0.534              
## overall_adhere  -0.945  0.311  0.234       
## overall_safety1  0.139 -0.079 -0.032 -0.205
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -3.43058828 -0.67881147  0.02915247  0.64404884  3.53027310 
## 
## Number of Observations: 540
## Number of Groups: 180

Blood PK

##              Model df      AIC      BIC    logLik   Test  L.Ratio p-value
## model            1  7 4860.258 4890.299 -2423.129                        
## model_large2     2 11 4851.039 4898.246 -2414.519 1 vs 2 17.21954  0.0018

## Linear mixed-effects model fit by maximum likelihood
##   Data: merged 
##        AIC      BIC    logLik
##   4860.258 4890.299 -2423.129
## 
## Random effects:
##  Formula: ~1 | ptid
##         (Intercept) Residual
## StdDev:     4.74164 21.00209
## 
## Fixed effects:  bloodVL_change ~ treatment + overall_adhere + overall_safety 
##                     Value Std.Error  DF   t-value p-value
## (Intercept)      98.73209  5.172962 356 19.086184  0.0000
## treatmentGel B   -6.81051  2.354117 356 -2.893020  0.0041
## treatmentGel C   -9.10003  2.295483 356 -3.964320  0.0001
## overall_adhere    0.93216  0.187884 356  4.961396  0.0000
## overall_safety1 -26.34806  3.460017 356 -7.615009  0.0000
##  Correlation: 
##                 (Intr) trtmGB trtmGC ovrll_
## treatmentGel B  -0.513                     
## treatmentGel C  -0.443  0.538              
## overall_adhere  -0.949  0.327  0.247       
## overall_safety1  0.131 -0.079 -0.032 -0.195
## 
## Standardized Within-Group Residuals:
##           Min            Q1           Med            Q3           Max 
## -3.5553528690 -0.5673073777  0.0005900677  0.6043037231  3.0550971969 
## 
## Number of Observations: 540
## Number of Groups: 180

## Linear mixed-effects model fit by maximum likelihood
##   Data: merged 
##        AIC      BIC    logLik
##   4851.039 4898.246 -2414.519
## 
## Random effects:
##  Formula: ~1 | ptid
##         (Intercept) Residual
## StdDev:    5.176441 20.56066
## 
## Fixed effects:  bloodVL_change ~ treatment * overall_adhere + treatment * overall_safety 
##                                    Value Std.Error  DF   t-value p-value
## (Intercept)                    131.74236 14.431943 352  9.128525  0.0000
## treatmentGel B                 -39.19101 15.315595 352 -2.558895  0.0109
## treatmentGel C                 -52.11513 15.650359 352 -3.329964  0.0010
## overall_adhere                  -0.36462  0.545375 352 -0.668563  0.5042
## overall_safety1                -11.39117  5.811353 352 -1.960158  0.0508
## treatmentGel B:overall_adhere    1.31391  0.591905 352  2.219795  0.0271
## treatmentGel C:overall_adhere    1.73440  0.603583 352  2.873511  0.0043
## treatmentGel B:overall_safety1 -25.67859  8.049524 352 -3.190076  0.0016
## treatmentGel C:overall_safety1 -17.98165  8.518057 352 -2.111003  0.0355
##  Correlation: 
##                                (Intr) trtmGB trtmGC ovrll_ ovrl_1 trGB:_ trGC:_
## treatmentGel B                 -0.924                                          
## treatmentGel C                 -0.901  0.841                                   
## overall_adhere                 -0.993  0.919  0.895                            
## overall_safety1                 0.113 -0.109 -0.107 -0.147                     
## treatmentGel B:overall_adhere   0.895 -0.986 -0.816 -0.901  0.138              
## treatmentGel C:overall_adhere   0.875 -0.818 -0.988 -0.881  0.135  0.804       
## treatmentGel B:overall_safety1 -0.080  0.118  0.075  0.104 -0.717 -0.173 -0.096
## treatmentGel C:overall_safety1 -0.075  0.073  0.113  0.098 -0.678 -0.093 -0.160
##                                tGB:_1
## treatmentGel B                       
## treatmentGel C                       
## overall_adhere                       
## overall_safety1                      
## treatmentGel B:overall_adhere        
## treatmentGel C:overall_adhere        
## treatmentGel B:overall_safety1       
## treatmentGel C:overall_safety1  0.492
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -3.63070078 -0.59111860 -0.02603496  0.59219448  2.76927257 
## 
## Number of Observations: 540
## Number of Groups: 180